SOLUTION: Foot of perpendicular drawn from pt. (2,3) to line x+y=11 is:

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Question 988954: Foot of perpendicular drawn from pt. (2,3) to line x+y=11 is:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Is this a question of the distance between the point and the line?

Given line y=-x%2B11, and a line perpendicular to it would have slope 1, which is negative reciprocal of -1.

Now, what is the equation for the line of slope -1 which goes through the given point (2,3)?
y-3=1%28x-2%29
y=x-2%2B3
y=x%2B1

FIND INTERSECTION POINT OF system%28y=x%2B1%2Cy=-x%2B11%29.
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Equating the two formulas for y,x%2B1=-x%2B11
2x%2B1=11
2x=10
x=5
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y=x%2B1
y=5%2B1
y=6
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Intersection point is (5,6).

DISTANCE FROM (5,6) TO (2,3):
Plug the values into the Distance Formula and evaluate or compute.
highlight%28sqrt%28%285-2%29%5E2%2B%286-3%29%5E2%29%29
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